In 1970, he married Kay Terry. They have three sons: Joseph, Brendan and Matthew. They are also the grandparents of their first grandchild, Julia Kaylin Amicone.

In November 2011, at the end of Amicone’s second and final term in office, the City Council voted to settle a federal court verdict against Mayor Phil Amicone for illegally pulling copies of a newspaper that was sharply critical of him off city streets. The paper claimed Amicone in 2007 ordered city employees to scoop up news racks and police to ticket newspaper distributors after the Westchester Guardian ran articles and headlines sharply critical of him.

The settlement required the city to pay $393,000 in damages to readers and employees of the weekly Westchester Guardian. But it would not hold the mayor personally liable — even though he was the main target of the newspaper's original lawsuit. The settlement would override a $170,000 personal judgment of punitive damages against Amicone made as part of the case that was set to be finalized by a federal judge.

In April 2013, the Yonkers City Council again voted to pass a $100,000 settlement to be paid by the Yonkers taxpayers, again on behalf of former mayor Amicone, for his making false defamatory comments against Mr. Zherka, publisher of the Westchester Guardian, as part of a separate lawsuit filed against Mr. Amicone. The entire defense for the former mayor was funded by the City of Yonkers, even though he was the main target of the lawsuits.